Question: All of the 4th grade teachers and students from Almond went on a field trip to an archaeology museum. Tickets were $$5.50$ each for teachers and $$2.50$ each for students, and the group paid $$47.00$ in total. The next month, the same group visited a science museum where the tickets cost $$22.00$ each for teachers and $$11.00$ each for students, and the group paid $$198.00$ in total. Find the number of teachers and students on the field trips.
Solution: Let $x$ equal the number of teachers and $y$ equal the number of students. The system of equations is: ${5.5x+2.5y = 47}$ ${22x+11y = 198}$ Solve for $x$ and $y$ using elimination. Multiply the top equation by $-4$ ${-22x-10y = -188}$ ${22x+11y = 198}$ Add the top and bottom equations together. ${y = 10}$ Now that you know ${y = 10}$ , plug it back into $ {5.5x+2.5y = 47}$ to find $x$ ${5.5x + 2.5}{(10)}{= 47}$ $5.5x+25 = 47$ $5.5x = 22$ $x = \dfrac{22}{5.5}$ ${x = 4}$ You can also plug ${y = 10}$ into $ {22x+11y = 198}$ and get the same answer for $x$ ${22x + 11}{(10)}{= 198}$ ${x = 4}$ There were $4$ teachers and $10$ students on the field trips.